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Results tagged with sequences-and-series
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user 466773
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
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answer
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Infinite series with inverse trigonometric functions
Consider the infinite series
$$
F(s)=\sum_{k=1}^\infty \frac{1}{k^{2s+1} \sin(k \pi \sqrt{2})}
$$
Prudnikov Vol.1 , gives a result for this sum in 5.4.16.13 for $s=1.$
$$
F(1)=-\frac{13 \pi^3}{360 \sq …
- 91